Beyond two-point statistics: using the minimum spanning tree as a tool for cosmology

Abstract

Cosmological studies of large scale structure have relied on 2-point statistics, not fully exploiting the rich structure of the cosmic web. In this paper we show how to capture some of this information by using the Minimum Spanning Tree (MST), for the first time using it to estimate cosmological parameters in simulations. Discrete tracers of dark matter such as galaxies, N-body particles or haloes are used as nodes to construct a unique graph, the MST, which is defined to be the minimum weighted spanning graph. We study the dependence of the MST statistics on cosmological parameters using haloes from a suite of COLA simulations with a box size of 250 h −1 Mpc that vary the amplitude of scalar fluctuations (A s ), matter density (Ω m ) and neutrino mass ( m ν ). The power spectrum P(k) and bispectrum B(k 1 , k 2 , k 3 ) are measured between k ∼ 0.125 and 0.5 hMpc −1 , while a corresponding lower cut of ∼ 12.6 h −1 Mpc is applied to the MST. The constraints from the individual methods are fairly similar but when combined we see improved 1σ constraints on Ω m of ∼ 17% with respect to P(k) and ∼ 12% with respect to P(k)+ B(k 1 , k 2 , k 3 ) thus showing the MST is providing additional information not present in the power spectrum and bispectrum. The MST is a tool which can be used to constrain parameters and/or to test systematics in current and future galaxy surveys. This is especially applicable to spectroscopy surveys (BOSS, DESI, Euclid, PSF, WFIRST and 4MOST) where the MST can be applied in 3D comoving coordinates and photometric surveys (DES and LSST) in tomographic shells. The Python code, MiSTree, used to construct the MST and run the analysis, is made publicly available at https://knaidoo29.github.io/mistreedoc/.

Constraining the Neutrino Mass with the Drifting Coefficient of the Field Cluster Mass Function

“…To understand the advantage of using β(z) as a cosmology discriminator, it may be worth comparing β(z) with the standard diagnostics such as the linear density power spectrum, nonlinear density bi spectrum and cluster mass function. As for the linear density power spectrum, it deals with isotropically averaged densities and thus fail to capture independent information contained in the anisotropic nonlinear cosmic web about the background cosmology (Naidoo et al 2020). As for the nonlinear density bi spectrum that treats the nonlinear anisotropic density field, it is not readily observable, suffering from highly nonlinear halo bias and redshift space distortion effects.…”

“…In reality, the gravitational collapse proceeds in a nonspherical way, for which the actual critical density contrast, δ c , departs from the idealistic spherical threshold, δ sc . The cosmology dependence of δ c is expected to overwhelm that of δ sc , given that the degree of the non-sphericity of the collapse process is closely linked with the anisotropy of the cosmic web, which in turn possesses strong dependence on the background cosmology (e.g., Shim & Lee 2013;Naidoo et al 2020). Unlike δ sc , however, the value of δ c and its link to the initial conditions cannot be analytically derived from first principles due to the complexity associated with the non-spherical collapse process (Bond & Myers 1996).…”

MiSTree: a Python package for constructing and analysing Minimum Spanning Trees

“…The statistics calculated by MiSTree are extensively explored in Naidoo et al (2019) and found to significantly improve constraints on cosmological parameters when tested on simulations.…”

“…MiSTree enables a user to measure the statistics of the MST and provides classes for binning the MST statistics (into histograms) and plotting the distributions. Applying the MST will enable the inclusion of high-order statistics information from the cosmic web which can provide additional information to improve cosmological parameter constraints (Naidoo et al 2019). This information has not been fully exploited due to the computational cost of calculating N -point statistics.…”

Cosmology and neutrino mass with the Minimum Spanning Tree

“…Petri et al 2013), the 1D probability distribution function (Uhlemann et al 2019), marked power spectra (Massara et al 2020), machine learning (ML; e.g. Fluri et al 2018), and the Minimum Spanning Tree (MST; Naidoo et al 2020) -the focus of this paper.…”